uClibc now has a math library. muahahahaha!

 -Erik

1 files changed, 521 insertions, 0 deletions

diff --git a/libm/ldouble/mtstl.c b/libm/ldouble/mtstl.c
new file mode 100644
index 000000000..0cd6eed16
--- /dev/null
+++ b/libm/ldouble/mtstl.c
@@ -0,0 +1,521 @@
+/*   mtst.c
+ Consistency tests for math functions.
+
+ With NTRIALS=10000, the following are typical results for
+ an alleged IEEE long double precision arithmetic:
+
+Consistency test of math functions.
+Max and rms errors for 10000 random arguments.
+A = absolute error criterion (but relative if >1):
+Otherwise, estimate is of relative error
+x =   cbrt(   cube(x) ):  max = 7.65E-20   rms = 4.39E-21
+x =   atan(    tan(x) ):  max = 2.01E-19   rms = 3.96E-20
+x =    sin(   asin(x) ):  max = 2.15E-19   rms = 3.00E-20
+x =   sqrt( square(x) ):  max = 0.00E+00   rms = 0.00E+00
+x =    log(    exp(x) ):  max = 5.42E-20 A rms = 1.87E-21 A
+x =   log2(   exp2(x) ):  max = 1.08E-19 A rms = 3.37E-21 A
+x =  log10(  exp10(x) ):  max = 2.71E-20 A rms = 6.76E-22 A
+x =  acosh(   cosh(x) ):  max = 3.13E-18 A rms = 3.21E-20 A
+x = pow( pow(x,a),1/a ):  max = 1.25E-17   rms = 1.70E-19
+x =   tanh(  atanh(x) ):  max = 1.08E-19   rms = 1.16E-20
+x =  asinh(   sinh(x) ):  max = 1.03E-19   rms = 2.94E-21
+x =    cos(   acos(x) ):  max = 1.63E-19 A rms = 4.37E-20 A
+lgam(x) = log(gamma(x)):  max = 2.31E-19 A rms = 5.93E-20 A
+x =  ndtri(   ndtr(x) ):  max = 5.07E-17   rms = 7.03E-19
+Legendre  ellpk,  ellpe:  max = 7.59E-19 A rms = 1.72E-19 A
+Absolute error and only 2000 trials:
+Wronksian of   Yn,   Jn:  max = 6.40E-18 A rms = 1.49E-19 A
+Relative error and only 100 trials:
+x = stdtri(stdtr(k,x) ):  max = 6.73E-19   rms = 2.46E-19
+*/
+
+/*
+Cephes Math Library Release 2.3:  November, 1995
+Copyright 1984, 1987, 1988, 1995 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+/* C9X spells lgam lgamma.  */
+#define GLIBC2 0
+
+#define NTRIALS 10000
+#define WTRIALS (NTRIALS/5)
+#define STRTST 0
+
+/* Note, fabsl may be an intrinsic function. */
+#ifdef ANSIPROT
+extern long double fabsl ( long double );
+extern long double sqrtl ( long double );
+extern long double cbrtl ( long double );
+extern long double expl ( long double );
+extern long double logl ( long double );
+extern long double tanl ( long double );
+extern long double atanl ( long double );
+extern long double sinl ( long double );
+extern long double asinl ( long double );
+extern long double cosl ( long double );
+extern long double acosl ( long double );
+extern long double powl ( long double, long double );
+extern long double tanhl ( long double );
+extern long double atanhl ( long double );
+extern long double sinhl ( long double );
+extern long double asinhl ( long double );
+extern long double coshl ( long double );
+extern long double acoshl ( long double );
+extern long double exp2l ( long double );
+extern long double log2l ( long double );
+extern long double exp10l ( long double );
+extern long double log10l ( long double );
+extern long double gammal ( long double );
+extern long double lgaml ( long double );
+extern long double jnl ( int, long double );
+extern long double ynl ( int, long double );
+extern long double ndtrl ( long double );
+extern long double ndtril ( long double );
+extern long double stdtrl ( int, long double );
+extern long double stdtril ( int, long double );
+extern long double ellpel ( long double );
+extern long double ellpkl ( long double );
+extern void exit (int);
+#else
+long double fabsl(), sqrtl();
+long double cbrtl(), expl(), logl(), tanl(), atanl();
+long double sinl(), asinl(), cosl(), acosl(), powl();
+long double tanhl(), atanhl(), sinhl(), asinhl(), coshl(), acoshl();
+long double exp2l(), log2l(), exp10l(), log10l();
+long double gammal(), lgaml(), jnl(), ynl(), ndtrl(), ndtril();
+long double stdtrl(), stdtril(), ellpel(), ellpkl();
+void exit ();
+#endif
+extern int merror;
+#if GLIBC2
+long double lgammal(long double);
+#endif
+/*
+NYI:
+double iv(), kn();
+*/
+
+/* Provide inverses for square root and cube root: */
+long double squarel(x)
+long double x;
+{
+return( x * x );
+}
+
+long double cubel(x)
+long double x;
+{
+return( x * x * x );
+}
+
+/* lookup table for each function */
+struct fundef
+	{
+	char *nam1;		/* the function */
+	long double (*name )();
+	char *nam2;		/* its inverse  */
+	long double (*inv )();
+	int nargs;		/* number of function arguments */
+	int tstyp;		/* type code of the function */
+	long ctrl;		/* relative error flag */
+	long double arg1w;		/* width of domain for 1st arg */
+	long double arg1l;		/* lower bound domain 1st arg */
+	long arg1f;		/* flags, e.g. integer arg */
+	long double arg2w;		/* same info for args 2, 3, 4 */
+	long double arg2l;
+	long arg2f;
+/*
+	double arg3w;
+	double arg3l;
+	long arg3f;
+	double arg4w;
+	double arg4l;
+	long arg4f;
+*/
+	};
+
+
+/* fundef.ctrl bits: */
+#define RELERR 1
+#define EXPSCAL 4
+
+/* fundef.tstyp  test types: */
+#define POWER 1 
+#define ELLIP 2 
+#define GAMMA 3
+#define WRONK1 4
+#define WRONK2 5
+#define WRONK3 6
+#define STDTR 7
+
+/* fundef.argNf  argument flag bits: */
+#define INT 2
+
+extern long double MINLOGL;
+extern long double MAXLOGL;
+extern long double PIL;
+extern long double PIO2L;
+/*
+define MINLOG -170.0
+define MAXLOG +170.0
+define PI 3.14159265358979323846
+define PIO2 1.570796326794896619
+*/
+
+#define NTESTS 17
+struct fundef defs[NTESTS] = {
+{"  cube",   cubel,   "  cbrt",   cbrtl, 1, 0, 1, 2000.0L, -1000.0L,   0,
+0.0, 0.0, 0},
+{"   tan",    tanl,   "  atan",   atanl, 1, 0, 1,    0.0L,     0.0L,  0,
+0.0, 0.0, 0},
+{"  asin",   asinl,   "   sin",    sinl, 1, 0, 1,   2.0L,     -1.0L,  0,
+0.0, 0.0, 0},
+{"square", squarel,   "  sqrt",   sqrtl, 1, 0, 1,  170.0L,    -85.0L, EXPSCAL,
+0.0, 0.0, 0},
+{"   exp",    expl,   "   log",    logl, 1, 0, 0,  340.0L,    -170.0L,  0,
+0.0, 0.0, 0},
+{"  exp2",   exp2l,   "  log2",   log2l, 1, 0, 0,  340.0L,    -170.0L,  0,
+0.0, 0.0, 0},
+{" exp10",  exp10l,   " log10",  log10l, 1, 0, 0,  340.0L,    -170.0L,  0,
+0.0, 0.0, 0},
+{"  cosh",   coshl,   " acosh",  acoshl, 1, 0, 0,  340.0L,     0.0L,  0,
+0.0, 0.0, 0},
+{"pow",       powl,      "pow",    powl, 2, POWER, 1, 25.0L, 0.0L,   0,
+50.0, -25.0, 0},
+{" atanh",  atanhl,   "  tanh",   tanhl, 1, 0, 1,    2.0L,    -1.0L,  0,
+0.0, 0.0, 0},
+{"  sinh",   sinhl,   " asinh",  asinhl, 1, 0, 1,  340.0L,   0.0L,  0,
+0.0, 0.0, 0},
+{"  acos",   acosl,   "   cos",    cosl, 1, 0, 0,   2.0L,      -1.0L,  0,
+0.0, 0.0, 0},
+#if GLIBC2
+  /*
+{ "gamma",  gammal,     "lgammal",   lgammal, 1, GAMMA, 0, 34.0, 0.0,   0,
+0.0, 0.0, 0},
+*/
+#else
+{ "gamma",  gammal,     "lgam",   lgaml, 1, GAMMA, 0, 34.0, 0.0,   0,
+0.0, 0.0, 0},
+{ "  ndtr",   ndtrl,  " ndtri",  ndtril, 1, 0, 1,  10.0L,  -10.0L,  0,
+0.0, 0.0, 0},
+{" ellpe",  ellpel,   " ellpk",  ellpkl, 1, ELLIP, 0,   1.0L, 0.0L,  0,
+0.0, 0.0, 0},
+{ "stdtr",  stdtrl,   "stdtri", stdtril, 2, STDTR, 1, 4.0L, -2.0L,   0,
+30.0, 1.0, INT},
+{ "  Jn",     jnl,   "  Yn",     ynl, 2, WRONK1, 0, 30.0,  0.1,  0,
+40.0, -20.0, INT},
+#endif
+};
+
+static char *headrs[] = {
+"x = %s( %s(x) ): ",
+"x = %s( %s(x,a),1/a ): ",	/* power */
+"Legendre %s, %s: ",		/* ellip */
+"%s(x) = log(%s(x)): ",		/* gamma */
+"Wronksian of %s, %s: ",  /* wronk1 */
+"Wronksian of %s, %s: ",  /* wronk2 */
+"Wronksian of %s, %s: ",  /* wronk3 */
+"x = %s(%s(k,x) ): ",	/* stdtr */
+};
+ 
+static long double y1 = 0.0;
+static long double y2 = 0.0;
+static long double y3 = 0.0;
+static long double y4 = 0.0;
+static long double a = 0.0;
+static long double x = 0.0;
+static long double y = 0.0;
+static long double z = 0.0;
+static long double e = 0.0;
+static long double max = 0.0;
+static long double rmsa = 0.0;
+static long double rms = 0.0;
+static long double ave = 0.0;
+static double da, db, dc, dd;
+
+int ldrand();
+int printf();
+
+int
+main()
+{
+long double (*fun )();
+long double (*ifun )();
+struct fundef *d;
+int i, k, itst;
+int m, ntr;
+
+ntr = NTRIALS;
+printf( "Consistency test of math functions.\n" );
+printf( "Max and rms errors for %d random arguments.\n",
+	ntr );
+printf( "A = absolute error criterion (but relative if >1):\n" );
+printf( "Otherwise, estimate is of relative error\n" );
+
+/* Initialize machine dependent parameters to test near the
+ * largest an smallest possible arguments.  To compare different
+ * machines, use the same test intervals for all systems.
+ */
+defs[1].arg1w = PIL;
+defs[1].arg1l = -PIL/2.0;
+/*
+defs[3].arg1w = MAXLOGL;
+defs[3].arg1l = -MAXLOGL/2.0;
+defs[4].arg1w = 2.0*MAXLOGL;
+defs[4].arg1l = -MAXLOGL;
+defs[6].arg1w = 2.0*MAXLOGL;
+defs[6].arg1l = -MAXLOGL;
+defs[7].arg1w = MAXLOGL;
+defs[7].arg1l = 0.0;
+*/
+
+/* Outer loop, on the test number: */
+
+for( itst=STRTST; itst<NTESTS; itst++ )
+{
+d = &defs[itst];
+m = 0;
+max = 0.0L;
+rmsa = 0.0L;
+ave = 0.0L;
+fun = d->name;
+ifun = d->inv;
+
+/* Smaller number of trials for Wronksians
+ * (put them at end of list)
+ */
+if( d->tstyp == WRONK1 )
+	{
+	ntr = WTRIALS;
+	printf( "Absolute error and only %d trials:\n", ntr );
+	}
+else if( d->tstyp == STDTR )
+	{
+	ntr = NTRIALS/100;
+	printf( "Relative error and only %d trials:\n", ntr );
+	}
+/*
+y1 = d->arg1l;
+y2 = d->arg1w;
+da = y1;
+db = y2;
+printf( "arg1l = %.4e, arg1w = %.4e\n", da, db );
+*/
+printf( headrs[d->tstyp], d->nam2, d->nam1 );
+
+for( i=0; i<ntr; i++ )
+{
+m++;
+k = 0;
+/* make random number(s) in desired range(s) */
+switch( d->nargs )
+{
+
+default:
+goto illegn;
+	
+case 2:
+ldrand( &a );
+a = d->arg2w *  ( a - 1.0L )  +  d->arg2l;
+if( d->arg2f & EXPSCAL )
+	{
+	a = expl(a);
+	ldrand( &y2 );
+	a -= 1.0e-13L * a * (y2 - 1.0L);
+	}
+if( d->arg2f & INT )
+	{
+	k = a + 0.25L;
+	a = k;
+	}
+
+case 1:
+ldrand( &x );
+y1 = d->arg1l;
+y2 = d->arg1w;
+x = y2 *  ( x - 1.0L )  +  y1;
+if( x < y1 )
+	x = y1;
+y1 += y2;
+if( x > y1 )
+	x = y1;
+if( d->arg1f & EXPSCAL )
+	{
+	x = expl(x);
+	ldrand( &y2 );
+	x += 1.0e-13L * x * (y2 - 1.0L);
+	}
+}
+
+/* compute function under test */
+switch( d->nargs )
+	{
+	case 1:
+	switch( d->tstyp )
+		{
+		case ELLIP:
+		y1 = ( *(fun) )(x);
+		y2 = ( *(fun) )(1.0L-x);
+		y3 = ( *(ifun) )(x);
+		y4 = ( *(ifun) )(1.0L-x);
+		break;
+#if 1
+		case GAMMA:
+		y = lgaml(x);
+		x = logl( gammal(x) );
+		break;
+#endif
+		default:
+		z = ( *(fun) )(x);
+		y = ( *(ifun) )(z);
+		}
+/*
+if( merror )
+	{
+	printf( "error: x = %.15e, z = %.15e, y = %.15e\n",
+	 (double )x, (double )z, (double )y );
+	}
+*/
+	break;
+	
+	case 2:
+	if( d->arg2f & INT )
+		{
+		switch( d->tstyp )
+			{
+			case WRONK1:
+			y1 = (*fun)( k, x ); /* jn */
+			y2 = (*fun)( k+1, x );
+			y3 = (*ifun)( k, x ); /* yn */
+			y4 = (*ifun)( k+1, x );	
+			break;
+
+			case WRONK2:
+			y1 = (*fun)( a, x ); /* iv */
+			y2 = (*fun)( a+1.0L, x );
+			y3 = (*ifun)( k, x ); /* kn */	
+			y4 = (*ifun)( k+1, x );	
+			break;
+
+			default:
+			z = (*fun)( k, x );
+			y = (*ifun)( k, z );
+			}
+		}
+	else
+		{
+		if( d->tstyp == POWER )
+			{
+			z = (*fun)( x, a );
+			y = (*ifun)( z, 1.0L/a );
+			}
+		else
+			{
+			z = (*fun)( a, x );
+			y = (*ifun)( a, z );
+			}
+		}
+	break;
+
+
+	default:
+illegn:
+	printf( "Illegal nargs= %d", d->nargs );
+	exit(1);
+	}	
+
+switch( d->tstyp )
+	{
+	case WRONK1:
+	/* Jn, Yn */
+/*	e = (y2*y3 - y1*y4) - 2.0L/(PIL*x);*/
+	e = x*(y2*y3 - y1*y4) - 2.0L/PIL;
+	break;
+
+	case WRONK2:
+/* In, Kn */
+/*	e = (y2*y3 + y1*y4) - 1.0L/x; */
+	e = x*(y2*y3 + y1*y4) - 1.0L;
+	break;
+	
+	case ELLIP:
+	e = (y1-y3)*y4 + y3*y2 - PIO2L;
+	break;
+
+	default:
+	e = y - x;
+	break;
+	}
+
+if( d->ctrl & RELERR )
+	{
+	if( x != 0.0L )
+		e /= x;
+	else
+		printf( "warning, x == 0\n" );
+	}
+else
+	{
+	if( fabsl(x) > 1.0L )
+		e /= x;
+	}
+
+ave += e;
+/* absolute value of error */
+if( e < 0 )
+	e = -e;
+
+/* peak detect the error */
+if( e > max )
+	{
+	max = e;
+
+	if( e > 1.0e-10L )
+		{
+da = x;
+db = z;
+dc = y;
+dd = max;
+		printf("x %.6E z %.6E y %.6E max %.4E\n",
+		da, db, dc, dd );
+/*
+		if( d->tstyp >= WRONK1 )
+			{
+		printf( "y1 %.4E y2 %.4E y3 %.4E y4 %.4E k %d x %.4E\n",
+		 (double )y1, (double )y2, (double )y3,
+		 (double )y4, k, (double )x );
+			}
+*/
+		}
+
+/*
+	printf("%.8E %.8E %.4E %6ld \n", x, y, max, n);
+	printf("%d %.8E %.8E %.4E %6ld \n", k, x, y, max, n);
+	printf("%.6E %.6E %.6E %.4E %6ld \n", a, x, y, max, n);
+	printf("%.6E %.6E %.6E %.6E %.4E %6ld \n", a, b, x, y, max, n);
+	printf("%.4E %.4E %.4E %.4E %.4E %.4E %6ld \n",
+		a, b, c, x, y, max, n);
+*/
+	}
+
+/* accumulate rms error	*/
+e *= 1.0e16L;	/* adjust range */
+rmsa += e * e;	/* accumulate the square of the error */
+}
+
+/* report after NTRIALS trials */
+rms = 1.0e-16L * sqrtl( rmsa/m );
+da = max;
+db = rms;
+if(d->ctrl & RELERR)
+	printf(" max = %.2E   rms = %.2E\n", da, db );
+else
+	printf(" max = %.2E A rms = %.2E A\n", da, db );
+} /* loop on itst */
+
+exit (0);
+return 0;
+}
+